We examine how the Supreme Court learns from lower court decisions to evaluate new legal issues. We present a theory of optimal stopping in which the Court learns from successive rulings on new issues by lower courts, but incurs a cost when lower courts come into conflict with one another. The Court faces a strategic trade-off between allowing conflict to continue while it learns about a new legal issue and intervening to end a costly conflict between the lower courts. We evaluate how factors such as the quality of lower courts, the distribution of judicial preferences, and the timing of the emergence of conflict affect how the Court weighs this trade-off. We provide empirical evidence that supports one of the theory's novel predictions: the Supreme Court should be more likely to end a conflict immediately when it emerges after several lower courts have already weighed in on a new legal issue, compared to when a conflict emerges early in the life of a legal issue.